1. Field of Endeavor
The invention relates to a gas turbine model and to a method for the modeling of a gas turbine.
2. Brief Description of the Related Art
The accurate simulation of the statics and dynamics of a gas turbine (GT) process is becoming increasingly important for the manufacturers and operators of gas turbines. GT process models are used, inter alia, for studying machine transients, for designing, testing and checking control logics of the control system of a gas turbine, and for developing training simulators for gas turbines. Also partly used are “real-time” GT processes, which are executed simultaneously with an actual turbine on a computer and serve in particular for the measurement signal conditioning, the online diagnosis, the model-based protection of a gas turbine, and also the improvement of the performance of a closed loop control of a gas turbine.
It is known that a gas turbine has a thermodynamic process, which includes a heat and mass transfer and chemical reactions. The physical laws controlling this process are expressed by partial differential equations. As a controlled object, a gas turbine constitutes a time-variant, nonlinear and dynamic Multiple-Input/Multiple-Output system with distributed parameters. Typically there is no analytical solution for a set of partial differential equations, such as the state equations of a gas turbine. The equations therefore have to be solved numerically.
For example, by assuming a gas turbine to be a lumped parameter system, the process of a gas turbine can be described by normal differential equations, as shown in equations 1:{dot over (x)}(t)=f(u(t),x(t),t)y(t)=g(u(t),x(t),t)  Equation 1,where t is the time, x(t) and {dot over (x)}(t) are vectors of system states and their derivatives with respect to time, and where u(t) is the input vector of the system and y(t) is the output vector of the system.
During startup, the warm-up phase, and during significant load changes, a gas turbine is a time-variant system. Significant load changes, which lead to noticeable influence in this context, are typically larger than 10% relative load. For most applications they even need to be larger than 20% or 30% relative load in order to have a noticeable influence. After a few hours of steady state operation, a gas turbine can be regarded as time-invariant. Its state equations can then be described according to equation 2:{dot over (x)}(t)=f(u(t),x(t))y(t)=g(u(t),x(t))  Equation 2.
To solve a set of nonlinear first-order differential equations, like equation 2, numerical methods, such as Gear Solver for example, are available. However, these methods require very complex numerical calculations. Furthermore, the identifying and verification of a model using these methods is difficult and time-consuming.
In order to reduce the solution complexity, the state equations of a gas turbine are normally simplified in order to form a linear or static model. The assumption of linearity is valid if the gas turbine works steady state close to a predefined operating point. The model error becomes greater if the gas turbine operates further away from this point or with fast transients. A static model cannot simulate the dynamics of the gas turbine process accurately.
Exemplary simplified gas turbine models are, for example, known from U.S. Pat. No. 7,219,040. Numerical solutions based on simplified linearized equations and complex nonlinear models are discussed.